login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Primes that are not squares mod 19.
4

%I #21 May 22 2022 09:49:40

%S 2,3,13,29,31,37,41,53,59,67,71,79,89,97,103,107,109,113,127,151,167,

%T 173,179,181,193,211,223,227,241,257,269,281,293,307,317,331,337,373,

%U 379,383,401,409,421,431,433,439,449,487,509,521,523,547,563,569,599

%N Primes that are not squares mod 19.

%C Inert rational primes in the field Q(sqrt(-19)). - _N. J. A. Sloane_, Dec 25 2017 [Corrected by _Jianing Song_, Dec 24 2018]

%C Primes p such that p^9 == -1 (mod 19). Primes congruent to {2, 3, 8, 10, 12, 13, 14, 15, 18} modulo 19. - _Jianing Song_, Dec 24 2018

%H Vincenzo Librandi, <a href="/A191063/b191063.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="https://oeis.org/index/Pri#primes_decomp_of">Index to sequences related to decomposition of primes in quadratic fields</a>

%t Select[Prime[Range[200]], JacobiSymbol[#,19]==-1&]

%o (Magma) [p: p in PrimesUpTo(599) | JacobiSymbol(p, 19) eq -1]; // _Vincenzo Librandi_, Sep 11 2012

%o (PARI) isok(p) = isprime(p) && !issquare(Mod(p, 19)); \\ _Michel Marcus_, Dec 25 2018

%K nonn,easy

%O 1,1

%A _T. D. Noe_, May 25 2011